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Compact Stars Compact Stars Lecture 12 Summary of the previous lecture I talked about neutron stars, their internel structure, the types of equation of state, and resulting maximum mass (Tolman-Openheimer-Volkoff limit) The neutron star EoS can be constrained if we know mass and/or radius of a star from observations Neutron stars exist in isolation, or are in binaries with MS stars, compact stars, including other NS. These binaries are final product of common evolution of the binary system, or may be a result of capture. Binary NS-NS merger leads to emission of gravitational waves, and also to the short gamma ray burst. The follow up may be observed as a ’kilonova’ due to radioactive decay of high-mass neutron-rich isotopes ejected from merger GRBs and cosmology In 1995, the 'Diamond Jubilee' debate was organized to present the issue of distance scale to GRBs It was a remainder of the famous debate in 1920 between Curtis and Shapley. Curtis argued that the Universe is composed of many galaxies like our own, identified as ``spiral nebulae". Shapley argued that these ``spiral nebulae" were just nearby gas clouds, and that the Universe was composed of only one big Galaxy. Now, Donald Lamb argued that the GRB sources were in the galactic halo while Bodhan Paczyński argued that they were at cosmological distances. B. Paczyński, M. Rees and D. Lamb GRBs and cosmology The GRBs should be easily detectable out to z=20 (Lamb & Reichart 2000). GRB 090429: z=9.4 The IR afterglows of long GRBs can be used as probes of very high z Universe, due to combined effects of cosmological dilation and decrease of intensity with time. Relation between peak energy of the GRB spectrum and the isotropic equivalent energy in the rest frame of the source (Ghirlanda et al. 2004) can make GRBs the relative 'standard candles'. If detected by gravitational wave detectors, the short GRBs could be 'absolute standard candles'. Very High z Universe At recombination, z~1100, the Universe becomes transparent. The cosmic backgroound radiation originates. When temperature of this radiation drops below 3000 K, there is no visible light ('Dark ages') First light occurs at z~20, when Lamb D Phil. Trans. R. Soc. A 2007;365:1363-1376 first stars form. Their UV radiation reionizes the Universe. High redshift Universe GRBs and cosmology Cosmological questions that may be addressed by observations of GRBs are: Moment of first light and earliest stars generation Star-formation history of the Universse: rate of GRBs with redshift Heavy element history of the Universe: by observing metal absorption line systems in spectra of GRB afterglows (Savaglio et al. 2006) Reionisation history of the Universe, by observing the red damping wing of the Gunn-Peterson through in GRB afterglow spectra (Lamb & Haiman 2003) Gunn-Peterson effect Neutral Hydrogen is present in the intergalactic medium. In spectra of quasars, the light is absorbed at wavelengths less than the Lyman-alpha edge, for a given redshift Effect was predicted by Gunn & Peterson (1965) First observed in 2001 in the SDSS (Sloan Digital Sky Survey) spectrum of a quasar with z=6.28, where the flux was zero beyond Lya z=6.28 quasar spectrum Becker R., et al. (2001, ApJ) Cosmic reionisation After recombination, the Hydrogen in the universe was neutral, until the radiation from first galaxies ionised again the intergalactic medium The Hydrogen must have been ionized again around z=6, as proved by the Gunn-Peterson through They showed that the scattering optical depth in the medium with even a small contribution of neutral H is huge and effectively would suppress the light observed from first quasars WMAP WMAP (Wilkinson Microwave Anisotropy Probe) satellite prove the cosmic reionisation must have happened at around z~6 GRBs and reionisation Volume averaged fraction of neutral IGM vs. Redshift (Fan et al. 2006). Solid line shows the model of Cen (2003) and dashed line is the model of Gnedin (2004). Spectrum of GRB 050904 (redshift z=6.3). Strong metal absorptiton lines and absorption due to Lya and Lyb (Kawai et al. 2006) Dark energy constraints Cosmological constraints for dark energy EOS parameters (w), from type Ia supernovae, long GRBs and combined, assuming H =65 km/s/Mpc and W = 0.27 (Ghirlanda et al. 2004). 0 M See also Firmani et al. (2006), and Riess et al. (2004). Break Binary black holes Binary black holes may exist in the nuclei of merged galaxies. Galaxy mergers are classified to: - minor mergers (one of the galaxies is much smaller than ”Mice galaxies”: two galaxies the other) and major mergers in a process of merger (similar sizes) - wet mergers (black holes merge in a gas rich environment) and dry mergers (galaxies are gas-poor) Binary black holes After merger, the product black hole receives the recoil kick velocity. Its magnitude depends on former spins of the merging components. The spin evolution proceeds inside a circumnuclear disc, relic of a gas-rich galaxy merger. As the black hole mass grows, its spin changes in strength and direction due to its gravito- magnetic coupling with the small-scale accretion disc. Dotti et al. (2009) Gravitational recoil of black holes SDSS J092712.65+294344.0 as the best candidate to date for a recoiling supermassive black hole (SMBH) Observations of emission lines from the source suggest that this might have been a gravitationally recoiled AGN nucleus (Komossa et al. 2008). Broad Balmer and broad high-ionization forbidden lines which are blueshifted by 2650 km s-1 relative to the set of narrow emission lines. This observation is most naturally explained if the SMBH was ejected from the core of the galaxy, carrying with it the broad-line gas while leaving behind the bulk of the narrow-line gas. Spectrum of SDSS J092712.65+294344.0 Two sets of emission lines separated by a velocity of 2650 km/s. Red: Red set of narrow emission lines (r-NELs). Blue and light blue: Blue set of emission lines (b- NELs and BELs, respectively). Gray: Fe II spectrum. NGC 1128 Abel 400 is a galaxy cluster Two merging galaxies there are seen as object NGC 1128, and in radio band identified as 3C 75 Four jets indicate presence of two accreting black holes X-ray image (blue) and radio image (pink color) NGC 326 ”X-shaped” morphology seen on radio maps Kinked jet, two fainter lobes oriented with an angle w.r.t brighter ones Possible effect of the past merger M60-UCD1 Ultra-compact dwarf galaxy in the Virgo cluster Contains a supermassive black hole with mass 2.1e7 Msun. Black hole contains about 20% of mass of this galaxy X-ray image: M. Kunert- Its relative velocity w.r.t center to the galaxy is Bajraszewska about 240 km/s Orphan black hole ejected from the host? Stable numerical schemes for BBH mergers Must choose the coordinates and systems of viariables that do not develop pathologies when the system is evolved The system of hyperbolic and elliptic equations is solved for constrained evolution The scheme must deal with geometric singularities in black hole spacetimes Numerical relativity Two main schemes are used Generalized harmonic coordinates with constrained damping (Pretorius 2005) ”Moving punctures’ method with conformal connection functions to the standard equations (Shibata et al. 2006). The method is called BSSN (from the names of authors) Each equation contains hundreds terms, requiring on several thousand oating point operations per grid point with any evolution scheme Geometric singularities inside black holes are treated with ’excision’ or special criteria for the lapse and shift functions (’moving punctures’) Several orders of magnitude of relevant physical length need to be resolved. This is done with the Adaptive Mesh technique 3+1 decomposition Numerical implementation of the 3 + 1 split of Einstein equations, for solving the Cauchy initial value problem using the BSSN method. Formulation assumes that spacetime is foliated into a family of 3-dimensional spacelike hypersurfaces. Proposed by Arnowitt, Deser and Misner (ADM formulation). Fundamental variables in the BBH evolution are spatial metric γ and ij extrinsic curvature tensor K ij Einstein Toolkit package ● Einstein Toolkit computational framework: a family of codes for use in relativistic astrophysics based on nite dierence computation on a gridded mesh (Loefer et al. 2012). ● The Toolkit is supported by a distributed model, combining core support of software, tools, and documentation in its SVN and GIT repository with partnerships of developers ● The latest version named Tesla (16th) was released on Feb 2018 ● The code documentation can be found on http://www.einsteintoolkit.org Gravitational wave visualisation Visualisation: P. Sukova Gravitational recoil For non-spinning, unequal mass components, the kick velocity of remnant black hole occurs, due to asymmetric beaming of radiation ● Recoil speed computed to be up to 175 km/s for non- spinning, unequal mass components ● Typical values for spinning black holes of 100s km/s, but can be as large as 4000km/s for equal mass black holes with spins vectors anti-aligned and in the orbital plane ● The latest Sample orbits ● Orbits of the inspiraling black holes, for equal masses (left) and mass ratio M1/M2=3 (right). Apparent horizons are marked with dashed circles. Recoil of merger product marked with blue line on the right. Apparent horizons The apparent horizons are localized around the components of the BH system in each slice of time during the evolution, and around fnal merged black hole after it forms. The AH shape is given by a function r = h(angle), found by solving a nonlinear elliptic PDE in h on S2 The proper integrals over the isolated horizon are calculated to extract the values of mass and spin of the merged black hole (treated 'quasilocally'; Dreyer et al.
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